Induced arithmetic removal: complexity 1 patterns over finite fields
Name
1911.03427.pdf
Description
Submitted version
Size
356.35 KB
Format
Adobe PDF
Checksum (MD5)
132e002390960fca71211f532966bbd5
Author(s)
Fox, Jacob
Tidor, Jonathan
Zhao, Yufei
Date Issued
2022
Journal
Israel Journal of Mathematics
Publisher
Springer Science and Business Media LLC
Citation
Fox, Jacob, Tidor, Jonathan and Zhao, Yufei. 2022. "Induced arithmetic removal: complexity 1 patterns over finite fields." Israel Journal of Mathematics, 248 (1).
Version
Original manuscript
Abstract
We prove an arithmetic analog of the induced graph removal lemma for
complexity 1 patterns over finite fields. Informally speaking, we show that
given a fixed collection of $r$-colored complexity 1 arithmetic patterns over
$\mathbb F_q$, every coloring $\phi \colon \mathbb F_q^n \setminus\{0\} \to
[r]$ with $o(1)$ density of every such pattern can be recolored on an
$o(1)$-fraction of the space so that no such pattern remains.
MIT Department
Massachusetts Institute of Technology. Department of Mathematics
Terms of Use
Creative Commons Attribution-Noncommercial-Share Alike
Persistent DSpace Link
DOI of Published Version
https://doi.org/10.1007/S11856-022-2290-X
